Time Deformation and Term Structure of Interest Rates

Abstract

The paper approaches the modeling of the yield curve from a stochastic volatility perspective based on time deformation. The way in which we model time deformation is new and differs from alternatives that currently exist in the literature and is based on market microstructure theory of the impact of information flow on a market. We model the stochastic volatility process by modeling the instantaneous volatility as a function of price intensity in the spirit of Cho and Frees (1988), Engle and Russell (1998) and Gerhard and Hautsch (2002). One contribution of the paper therefore lies with the introduction of a new transaction level approach to the econometric modelling of stochastic volatility in a multivariate framework exploiting intensity-based point processes previously used by Bowsher (2003), Hall and Haustch (2003). We find that the individual yields of U.S. treasury notes and bonds appear to be driven by different operational clocks as suggested by the market segmentation theory of the Term Structure but these are related to each other through a multivariate Hawkes model which effectively coordinates activity along the yield curve. The results offer some support to the Market Segmentation or Preferred Habitat models as the univariate Hawkes models we have found at each maturity are statistically significantly different from each other and the major impact on each maturity is activity at that maturity. However there are flows between the different maturities that die away relatively quickly which indicates that the markets are not completely segmented. Diagnostic tests show that the point process models are relatively well specified and a robustness comparison with realized volatility indicates the close relationship between the two estimators of integrated volatility but also some differences between the structural intensity model and the model free realized volatility. We have also shown that bond returns standardized by the instantaneous volatility estimated from our Hawkes model are Gaussian which is consistent with the theory of time deformation for security prices quite generally.

Keywords: Term structure, Interest rates, Multivariate modeling, Hawkes process, Time deformation.

JEL Classification: C16, E43, F3, G1, G12